Pricing of Short Life-Cycle Products through Active Learning∗

Revenue management techniques, practiced for many years in the airline and hotel industries, have gained popularity with retailers. One such technique — dynamic pricing — refers to the intelligent process of controlling prices over a course of a sales season in a way that maximizes expected revenues. In this paper, we consider a retailer who sells a fashionable good during a short sales season, but is uncertain about how successful the product will be in the market. Will it attract customer attention or not? and to what extent? We propose a continuous-time revenue-maximization model in which the seller continuously learns about the market reaction to his product from sales observations. Customers arrive randomly over the course of the season, and each customer has an individual reservation price based on which he makes his own purchasing decision. We combine theoretical results with numerical experimentation to study the value of dynamic pricing for a retailer faced with market uncertainty. We compare optimal expected revenues to those obtained under three alternative pricing policies: fixed pricing schemes, certainty-equivalent policies, and naive pricing policies that completely ignore the existence of market uncertainty. The comparative study allows us to explore the value of proactively setting prices to impact the revenue as well as the learning process itself (“active learning”) versus “passive learning,” where learning is performed continuously, but the impact of prices on learning is ignored. We also consider the expected revenues under perfect information about the market condition.